Quantum and classical integrable sine-Gordon model with defect

TL;DR

This paper demonstrates the exact classical and quantum integrability of the sine-Gordon model with a defect, deriving R-matrices, algebraic structures, and conserved quantities, and analyzing defect-induced soliton dynamics.

Contribution

It establishes the integrability of the sine-Gordon model with a defect at both classical and quantum levels, including explicit R-matrices and conserved quantities.

Findings

Exact classical and quantum R-matrices derived.

Higher conserved quantities explicitly calculated.

Defect can create, annihilate, or preserve solitons with phase shifts.

Abstract

Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the quantum level based on the Yang-Baxter equation. We find the associated classical and quantum R-matrices and the underlying q-algebraic structures, analyzing the exact lattice regularized model. We derive algorithmically all higher conserved quantities $C_n, n=1,2,...$ of this integrable DSG model, focusing explicitly on the contribution of the defect point to each $C_n$. The bridging condition across the defect, defined through the B\"acklund transformation is found to induce creation or annihilation of a soliton by the defect point or its preservation with a phase shift.